Analytical solutions of fracture parameters for a centrally cracked Brazilian disk considering the loading friction

A centrally cracked Brazilian disk (CCBD) specimen subjected to a pair of diametral compressive forces has been widely used to study mixed-mode I and II fractures of brittle and quasi-brittle materials. Reasons for using the CCBD are mainly due to its capability to introduce different mode mixities from pure mode I to pure mode II, the existence of closed-form solutions for fracture parameters, and the simple setup of compressive test. In addition to the diametrical concentrated force loading, the partially distributed pressure loading is also an important loading condition for CCBD specimen tests. Using the weight function method, analytical solutions of stress intensity factors and T stress considering the tangential loading friction for a CCBD specimen that is subjected to four typical partially distributed loads were derived, and effects of the boundary friction and load distribution angle on the fracture parameters were also explored. The results obtained are as follows: (1) For short cracks, geometric parameters Y_I, Y_II, and T* of pure mode I and II fractures decrease with an increase in the friction coefficient and load distribution angle. However, for long cracks, an increase in the friction coefficient causes an increase in pure mode-I Y_I, and an increase in the load distribution angle causes an increase in pure mode-II T*; (2) The influence of the load distribution angle on the fracture parameters is the most significant when the distributed pressure follows a constant function form, while it is the least significant for the case of quartic polynomial pressure; (3) The critical loading angle for pure mode II fractures decreases with an increase in the load distribution angle for short cracks, whereas it increases for long cracks. When the load distribution angle is fixed, an increase in friction can raise the critical loading angle for pure mode II fractures. These results have further improved the research of fracture parameters in CCBD specimens.